(Part SP) Refer to the above figure, this model has [a] decision variables. 

Question 2.1.1   Joseph Priestley invented fizzy drinks by adding a gas he called ‘heavy air’. What is the name of the gas now? [ans1] (1)

Question 1.4.1 In solids, liquids and gases the particles behave in different ways. Describe how the particles in solids behave. (1)

[Part2] There are five corner points: (X1, X2)={(0,0),(8,0),(8,2),(4,6),(0,8)}.The optimal solution is ______________?

(Part SP) Consider the following shortest path problem where node 1 is the starting node and node 6 is the destination node. What is the constraint associated with node 1?

Question 1.4.3   Describe how the particles in liquids behave. (1)

Question 1.4.2   Describe how the particles in gases behave. (1)

The IP solution can sometimes produce a better objective function value than its LP relaxed problem.

[Part1] A redundant constraint is eliminated from a linear programming model. What effect will this have on the optimal solution?

(Part SA) If the profit for product X was reduced to $4 (i.e., $5 becomes  $4) while at the same time the profit for product Y was increased to $7 ($4 becomes  $7), the optimal solution values (i.e., X and Y) would be same. What is the value of “100% Rule”?